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Optimal (Degree+1)-Coloring in Congested Clique

Authors Sam Coy , Artur Czumaj , Peter Davies , Gopinath Mishra

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ACM Subject Classification
  • Theory of computation → Massively parallel algorithms
  • Theory of computation → Distributed algorithms
  • Theory of computation → Pseudorandomness and derandomization
  • Mathematics of computing → Graph algorithms
Keywords
  • Distributed computing
  • graph coloring
  • parallel computing

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Abstract

We consider the distributed complexity of the (degree+1)-list coloring problem, in which each node u of degree d(u) is assigned a palette of d(u)+1 colors, and the goal is to find a proper coloring using these color palettes. The (degree+1)-list coloring problem is a natural generalization of the classical (Δ+1)-coloring and (Δ+1)-list coloring problems, both being benchmark problems extensively studied in distributed and parallel computing.
In this paper we settle the complexity of the (degree+1)-list coloring problem in the Congested Clique model by showing that it can be solved deterministically in a constant number of rounds.

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Sam Coy, Artur Czumaj, Peter Davies, and Gopinath Mishra. Optimal (Degree+1)-Coloring in Congested Clique. In 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 261, pp. 46:1-46:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023) https://doi.org/10.4230/LIPIcs.ICALP.2023.46

Author Details

Sam Coy
  • University of Warwick, Coventry, UK
Artur Czumaj
  • University of Warwick, Coventry, UK
Peter Davies
  • Durham University, UK
Gopinath Mishra
  • University of Warwick, Coventry, UK

Funding

  • Coy, Sam: Research supported in part by the Centre for Discrete Mathematics and its Applications (DIMAP), by an EPSRC studentship, and by the Simons Foundation Award No. 663281 granted to the Institute of Mathematics of the Polish Academy of Sciences for the years 2021-2023.
  • Czumaj, Artur: Research supported in part by the Centre for Discrete Mathematics and its Applications, by EPSRC award EP/V01305X/1, by a Weizmann-UK Making Connections Grant, by an IBM Award, and by the Simons Foundation Award No. 663281 granted to the Institute of Mathematics of the Polish Academy of Sciences for the years 2021-2023.
  • Mishra, Gopinath: Research supported in part by the Centre for Discrete Mathematics and its Applications (DIMAP), by EPSRC award EP/V01305X/1, and by the Simons Foundation Award No. 663281 granted to the Institute of Mathematics of the Polish Academy of Sciences for the years 2021-2023.

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